Joseph P. Kennedy III, drawing heavily on his family’s national network of donors, raised $1.3 million in the first three months of this year to finance his bid to replace retiring US Representative Barney Frank.

Kennedy’s fund-raising numbers dwarf what other first-time Massachusetts congressional candidates have ever raised in their initial three months, campaign finance veterans said Friday.

His total donations also put him among the top tier of congressional candidates across the country this year, including House incumbents who have a big advantage in raising money.

“He would be in the top 10 percent if he were running for reelection as a House member,’’ said Doug Weber, a senior researcher at the Center for Responsive Politics, a nonpartisan, Washington-based group that monitors campaign contributions.

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The median fund-raising figure for cash raised in 2011 by incumbent House members is about $619,000, Weber said.

Kennedy’s campaign did not provide a breakdown of in-state vs. out-of-state donations.

But sources involved in Kennedy’s fund-raising said the 31-year-old candidate made fund-raising appearances around the country, using family connections from Florida; Washington, D.C.; and California to help raise money.

In 2010, when Bielat ran a spirited campaign against Frank, he, too, drew heavily on out-of-state resources. With national Republicans and cultural conservatives targeting Frank, Bielat collected more than $2.4 million in donations, most of them pouring in during the final months of the race.

He said his campaign’s average contribution so far this year has been $90.

Another Republican, psychiatrist Elizabeth Childs of Brookline, raised $43,000 in the first quarter, according to her campaign.

Kennedy’s campaign manager, Nick Clemons, said the candidate’s fund-raising demonstrated “a fantastic show of the kind of on-the-ground support this campaign is built on.’’

“The donations came from more than 1,500 individuals, nearly half of whom gave $100 or less,’’ Clemons said in an e-mail to Kennedy’s supporters.

“A lot of congressional campaigns would be happy to raise $1.3 million over the course of their entire race, let alone over one quarter,’’ said Rob Gray, a veteran Massachusetts Republican strategist.

“Clearly the Kennedy calling card still works in Massachusetts and across the country,’’ Gray said. “It is a very impressive haul.’’

None of the campaigns released a full listing of the candidates’ itemized donations. Candidates are required to file complete reports with the Federal Election Commission by Sunday.

Martin T. Meehan, the former Democratic congressman from Lowell who during his 14-year tenure built up the largest campaign account of any House member, said he is in awe of Kennedy’s fund-raising abilities.

“I don’t know anybody who has raised that much money in the first three months of a campaign,’’ said Meehan, who has advised the candidate and is now the chancellor of the University of Massachusetts Lowell.

Philip W. Johnston, a former state Democratic Party chairman who is part of Kennedy’s fund-raising operation, called his donation tally is “unprecedented’’ for a first time congressional candidate in Massachusetts.

Johnston said Kennedy’s success goes beyond the fact that he has access to a large network of family political financial backers. He said Kennedy, the son of former US Representative Joseph P. Kennedy II, is a natural at raising money.

“He is incredibly focused and disciplined,’’ said Johnston, a onetime congressional candidate. “Most candidates hate fund-raising and do everything to avoid it, but he is remarkably gifted at it.’’

Noah Bierman of the Globe staff contributed to this report. Frank Phillips can be reached at phillips@globe.com.

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